Finite Group Databasebeta

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C₂×#5101 #83726

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

592 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 25 points:

(3,4,5)(10,12,13,18,14,19,20,24)(11,16,17,23,15,21,22,25);(1,2)(10,11)(12,16)(13,17)(14,15)(18,23)(19,21)(20,22)(24,25);(4,5)(6,7,8,9)(11,15)(16,21)(17,22)(23,25);(1,2)

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 16302);